SOLUTION: Find a possible formula for the exponential function through the points (−2,54) and (2,6/9)

Algebra ->  Systems-of-equations -> SOLUTION: Find a possible formula for the exponential function through the points (−2,54) and (2,6/9)      Log On


   

Question 1155242: Find a possible formula for the exponential function through the points (−2,54) and (2,6/9)
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


y+=+ab%5Ex

Use the two given data points:

54+=+ab%5E%28-2%29
2%2F3+=+ab%5E2

Divide the second equation by the first:

1%2F81+=+b%5E4
1%2F3+=+b

Note if this were a geometric sequence problem, the value of b could be either 1/3 or -1/3. But for an exponential function, b has to be positive.

Substitute this value of b in either original equation to find a.

2%2F3+=+a%281%2F3%29%5E2
2%2F3+=+a%2F9
a+=+9%282%2F3%29+=+6

ANSWER: One possible function for the two given points is y+=+6%281%2F3%29%5Ex